A mobile is formed by supporting four metal butterflies of equal mass m from a s

Question

A mobile is formed by supporting four metal butterflies of equal mass m from a string of length L. The points of support are evenly spaced a distance lapart as shown below. The string forms an angle ?1with the ceiling at each endpoint. The center section of string is horizontal.

(a) Starting from left to right, find the tension in each of the five sections of string in terms of ?1, m, and g.

T1 =

T2 =

T3 =

T4 =

T5 =

(b) Find the angle ?2, in terms of ?1, that the sections of string between the outside butterflies and the inside butterflies form with the horizontal.

?2 =

(c) Show that the distance D between the endpoints of the string is as shown below. (Do this on paper. It will not count on your grade, but it will help you prepare for the test.)

D = (L/5) (2cos?1 + 2cos[tan-1(?tan?1)] + 1)

Explanation / Answer

Part A T1=2mg / sin(theta_1) T2=mg/sin(tan^-1(tan( (theta_1)/ 2 ))) T3=2mg/tan(theta_1) T4=mg/sin(tan^-1(tan( (theta_1)/ 2 ))) T5=2mg / sin(theta_1) Part B tan^-1(tan(theta_1)/2) Source: Physics for scientists and engineers 6th edition (Serway and Jewett) pg A.40 #73 See the following as the input is very picky.

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